What other people do doesn't matter.
If you're not happy being sexual with someone who 'doesn't like using condoms' then don't do it. If you want him to test before you do so, or if you do not trust him to be monogamous, stick to your boundaries.
Yep, in the UK, tests are unlikely to include HPV - 'a lot of partners' means he quite probably has it, so have you had the vaccine? - and HSV is diagnosed when cold sores appear.